image: Energy diagram illustrating the dependence of eigenstate energies on quasiperiodic potential strength. Red dashed lines show the existence of two mobility edges in the system.
Credit: ©Science China Press
The Quest for Mobility Edges
In quantum systems, particles are described by wavefunctions, which tell us where the particles are likely to be found. In a disordered material, these wavefunctions can either be localized, meaning the particle is confined to a specific region, or extended, allowing the particle to roam freely. The mobility edge is the critical boundary between these two behaviors. In three-dimensional systems, this boundary has been well-established, but in one-dimensional systems, it has long been believed that all states become localized in the presence of disorder—until now.
Recent breakthroughs in theoretical physics (Phys. Rev. Lett. 125, 196604) have shown that under certain conditions, even in one-dimensional systems, there can be multiple mobility edges. This discovery has inspired experimental physicists to explore the possibility of observing such transitions in real-world systems.
Quasiperiodic Mosaic Lattices: A New Frontier
The recent research published in Science Bulletin, conducted by a team from KTH Royal Institute of Technology, Nordita, and several international collaborators, focused on a special type of quantum system known as a quasiperiodic mosaic lattice. Unlike traditional lattices, which are either perfectly ordered or entirely disordered, quasiperiodic lattices feature a pattern that is almost—but not quite—repeating. The subtle complexity along with the mosaic modulation period makes them ideal for investigating the nuances of localization physics.
Using advanced nanophotonic circuits, the researchers were able to create a mosaic lattice in which they could precisely control the position and potential energy of each site. By modulating the potential in a quasiperiodic manner, they were able to observe the coexistence of both localized and extended states within the same system, providing direct evidence for multiple MEs.
Engineering Light to Explore Quantum Phenomena
The experiment relied on a platform of integrated silicon nitride photonic circuits, which are compatible with standard semiconductor manufacturing techniques. This allowed the team to design a lattice with nanoscale precision. By injecting light into individual sites of the lattice and observing how it propagated, the researchers could probe the underlying quantum states.
Their observations revealed that at certain energy levels, the wavefunctions were confined to specific regions of the lattice, indicating localization. However, at other energies, the wavefunctions spread out across the entire lattice, signifying extended states. The transition between these two behaviors corresponded to the mobility edges predicted by theory.
“Our work provides direct experimental evidence that multiple mobility edges can exist in a single system,” said Jun Gao, the lead author and researcher at KTH Royal Institute of Technology. “To the best of our knowledge, our implementation represents the first experimental investigation of ME physics using integrated photonic chips, offering a practical means of controlling lattice parameters within a wide tunable range at room temperature in contrast to cold atomic systems.”
“The key was to break the duality symmetry of the lattice and introduce varying modulation periods,” explained co-author Prof. Ivan M. Khaymovich from Nordita, Stockholm University. “This enabled us to observe how extended states can survive even in regimes of strong quasiperiodic potential, a phenomenon not seen in previous models.”
The discovery of multiple MEs in quasiperiodic mosaic lattices is more than just a fascinating piece of quantum physics—it has practical implications for the development of future quantum technologies. Understanding how particles behave in disordered systems is crucial for designing robust quantum devices, including quantum computers and sensors, which must operate reliably in the presence of noise and other imperfections.
Moreover, the experimental approach demonstrated in this study showcases the power of integrated photonic platforms for exploring complex quantum phenomena. These platforms are scalable, meaning they can be expanded to create larger and more sophisticated quantum systems. This opens up exciting possibilities for simulating other quantum systems that are currently beyond the reach of classical computers.
Journal
Science Bulletin